Question

Below are the steps to solve an equation:

Step 1: |x - 4| + 1 = 8
Step 2: |x - 4| = 8 - 1
Step 3: |x - 4| = 7

Which of the following is a correct next step to solve the equation?

Answer 1

A correct next step is to add 4 to both sides to get x = 11.

Answer 2

I disagree.

Answer 3

@RyleeC explain your reasoning then

Answer 4

So okay

Answer 5

Absolute value must always be solved inside then pulled out as positive. Therefore x-4 must be positive, but must be subtracted first. So you would have to minus 7 by 4, to get x = 3

Answer 6

So would I do 7 -4

Answer 7

I know, but let's say that x = 11, like I said earlier. If you take |11 - 4| = 7, the absolute value of 11 - 4 is 7.

Answer 8

You can even go all the way back and do that. |11 - 4| + 1 = 8, 7 + 1 = 8, 8 = 8.

Answer 9

But if x is -3 the absolute value would still be 7 since -3 - 4 is -7 but become +7 due to absolute value.

Answer 10

SO would the next step be x + 4 = 7

Answer 11

Ok, then. Let me solve it here (for is x = -3). |-3 + 4| + 1 = 8, |4 - 3| + 1 = 8, 1 + 1 = 8, 2 ≠ 8

Answer 12

It works both ways x=-3, and 11. Therefore the correct step is to minus the 4 from both sides, to theoretically minus out the absolute value of a -4.

Answer 13

You messed up your signs above^

Answer 14

No, I just explained that -3 won't be an acceptable answer ^^^

The correct answer is x = 11, because you ADD 4, because on the left side, it's being SUBTRACTED.

Answer 15

wht do u meen by meh messing up meh signs?

Answer 16

You incorrectly explained the -3 because your signs are wrong.

Answer 17

-3-4 is -7 which turns into 7 due to the absolute value and 7 = 7.

Answer 18

The answeres are
x - 4 = -7

x + 4 = -7

-x - 4 = 7

x + 4 = 7

Answer 19

Its not -3 + 4.

Answer 20

Oh, derp. So, x = -3 and x = 11.

Answer 21

YES! ahaha

Answer 22

There's multiple answers.

Answer 23

Yep.

Answer 24

Its D.

Answer 25

Thank you

Answer 26

Welcome. :)

Answer 27

Heres why. The technical correct way it to minus the 4, this takes the absolute value into consideration.

Answer 28

D is the only answer that considers that step.